In the recent past, finding robust solutions for optimization problems contaminated with uncertainties has been topical and has been investigated in the literature for scalar and multi-objective/vector-valued optimization problems. In this paper, we introduce various types of robustness concept for set-valued optimization, such as min–max set robustness, optimistic set robustness, highly set robustness, flimsily set robustness, multi-scenario set robustness. We study some existence results for corresponding concepts of solution and establish some relationship among them.

中文翻译：

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关于集值优化问题的鲁棒性

在最近的过去中，寻找针对不确定性污染的优化问题的鲁棒解决方案已经成为热门话题，并且已经在文献中针对标量和多目标/向量值优化问题进行了研究。在本文中，我们介绍了用于集值优化的各种类型的鲁棒性概念，例如最小-最大集鲁棒性，乐观集鲁棒性，高度集鲁棒性，脆弱集鲁棒性，多场景集鲁棒性。我们研究了相应解的存在性结果，并建立了它们之间的联系。